메뉴 건너뛰기




Volumn 24, Issue 5, 2011, Pages 1655-1682

Canards and curvature: Nonsmooth approximation by pinching

Author keywords

[No Author keywords available]

Indexed keywords


EID: 79955055029     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/24/5/014     Document Type: Article
Times cited : (24)

References (28)
  • 1
    • 0001938848 scopus 로고
    • Chasse au Canard
    • Benòt E, Callot J-L, Diener F and Diener M 1981 Chasse au Canard Collect. Math. 31-32 37-119
    • (1981) Collect. Math. , vol.31-32 , pp. 37-119
    • Benòt E, C.1
  • 2
    • 0013630323 scopus 로고
    • Canard explosion and excitation in a model of the Belousov-Zhabotinskii reaction
    • Brns M and Bar-Eli K 1991 Canard explosion and excitation in a model of the Belousov-Zhabotinskii reaction J. Phys. Chem. 95 8706-13
    • (1991) J. Phys. Chem. , vol.95 , Issue.22 , pp. 8706-8713
    • Brns, M.1    Bar-Eli, K.2
  • 3
    • 0041757877 scopus 로고    scopus 로고
    • Structural stability of piecewise smooth systems
    • Broucke M E, Pugh C C and Simić S N 2001 Structural stability of piecewise smooth systems Comput. Appl. Math. 20 51-90
    • (2001) Comput. Appl. Math. , vol.20 , pp. 51-90
    • Broucke M E, P.1
  • 6
    • 80051722401 scopus 로고    scopus 로고
    • Canards and curvature: The 'smallness of ε' in slow-fast dynamics
    • Desroches M and Jeffrey M R 2011 Canards and curvature: the 'smallness of ε' in slow-fast dynamics Proc. R. Soc. A submitted
    • (2011) Proc. R. Soc.
    • Desroches, M.1    Jeffrey, M.R.2
  • 7
    • 0001356311 scopus 로고
    • Persistence and smoothness of invariant manifolds for flows
    • Fenichel N 1972 Persistence and smoothness of invariant manifolds for flows Indiana Univ. Math. J. 21 193-226
    • (1972) Indiana Univ. Math. J. , vol.21 , Issue.3 , pp. 193-226
    • Fenichel, N.1
  • 8
    • 34250627892 scopus 로고
    • Geometric singular perturbation theory for ordinary differential equations
    • Fenichel N 1979 Geometric singular perturbation theory for ordinary differential equations J. Diff. Eqns 31 53-98
    • (1979) J. Diff. Eqns , vol.31 , Issue.1 , pp. 53-98
    • Fenichel, N.1
  • 10
    • 53349102813 scopus 로고
    • Impulses and physiological states in theoretical models of nerve membrane
    • FitzHugh R 1961 Impulses and physiological states in theoretical models of nerve membrane Bioophys. J. 1 445-66
    • (1961) Bioophys. J. , vol.1 , Issue.6 , pp. 445-466
    • Fitzhugh, R.1
  • 11
  • 12
    • 84967355760 scopus 로고    scopus 로고
    • The development of the Hindmarsh-Rose model for bursting
    • ed S Coombes and P C Bressloff (Singapore: World Scientific)
    • Hindmarsh J L and Cornelius P 2005 The development of the Hindmarsh-Rose model for bursting Bursting: The Genesis of Rhythm in the Nervous System ed S Coombes and P C Bressloff (Singapore: World Scientific) pp 3-18
    • (2005) Bursting: The Genesis of Rhythm in the Nervous System , pp. 3-18
    • Hindmarsh, J.L.1    Cornelius, P.2
  • 13
    • 0021768729 scopus 로고
    • A model of neuronal bursting using three coupled first-order differential equations
    • Hindmarsh J L and Rose R M 1984 A model of neuronal bursting using three coupled first-order differential equations Proc. R. Soc. Lond. B 221 87-102
    • (1984) Proc. R. Soc. Lond. , vol.221 , Issue.1222 , pp. 87-102
    • Hindmarsh, J.L.1    Rose, R.M.2
  • 15
    • 0000303940 scopus 로고    scopus 로고
    • Neural excitability, spiking, and bursting
    • Izhikevich E 2000 Neural excitability, spiking, and bursting Int. J. Bifurcation Chaos 10 1171-266
    • (2000) Int. J. Bifurcation Chaos , vol.10 , Issue.6 , pp. 1171-1266
    • Izhikevich, E.1
  • 16
    • 79955070557 scopus 로고    scopus 로고
    • The geometry of generic sliding bifurcations
    • Jeffrey M R and Hogan S J 2011 The geometry of generic sliding bifurcations SIAM Rev. at press
    • (2011) SIAM Rev.
    • Jeffrey, M.R.1    Hogan, S.J.2
  • 17
    • 66149089209 scopus 로고    scopus 로고
    • The two-fold singularity of discontinuous vector fields
    • Jeffrey M R and Colombo A 2009 The two-fold singularity of discontinuous vector fields SIAM J. Appl. Dyn. Syst. 8 624-40
    • (2009) SIAM J. Appl. Dyn. Syst. , vol.8 , Issue.2 , pp. 624-640
    • Jeffrey, M.R.1    Colombo, A.2
  • 18
    • 0002316532 scopus 로고
    • Geometric singular perturbation theory
    • (Lecture Notes in Mathematics) (Berlin: Springer)
    • Jones C K R T 1995 Geometric singular perturbation theory Dynamical Systems (Montecatini Terme, Italy, 1994) (Lecture Notes in Mathematics vol 1609) (Berlin: Springer) pp 44-118
    • (1995) Dynamical Systems (Montecatini Terme, Italy, 1994) , vol.1609 , pp. 44-118
    • Jones, C.K.R.T.1
  • 19
    • 0002115697 scopus 로고    scopus 로고
    • An introduction to geometric methods and dynamical systems theory for singular perturbation problems
    • (Proceedings of Symposia Applied Mathematics) (Providence, RI: American Mathematical Society)
    • Kaper T J 1999 An introduction to geometric methods and dynamical systems theory for singular perturbation problems Analyzing Multiscale Phenomena Using Singular Perturbation Methods (Baltimore, MD, 1998) (Proceedings of Symposia Applied Mathematics vol 56) (Providence, RI: American Mathematical Society) pp 85-131
    • (1999) Analyzing Multiscale Phenomena Using Singular Perturbation Methods (Baltimore, MD, 1998) , vol.56 , pp. 85-131
    • Kaper, T.J.1
  • 20
    • 55949135112 scopus 로고    scopus 로고
    • Mixed-mode oscillations in three time-scale systems: A prototypical example
    • Krupa M, Popović N and Kopell N 2008 Mixed-mode oscillations in three time-scale systems: a prototypical example SIAM J. Appl. Dyn. Syst. 7 361-402
    • (2008) SIAM J. Appl. Dyn. Syst. , vol.7 , Issue.2 , pp. 361-402
    • Krupa M, P.1
  • 21
    • 0000833107 scopus 로고
    • Etude des oscillations auto entretenues
    • Línard A 1928 Etude des oscillations auto entretenues Rev. Ǵn. l'Electr. 23 901-12
    • (1928) Rev. Ǵn. l'Electr. , vol.23 , pp. 901-912
    • Línard, A.1
  • 22
    • 65249132884 scopus 로고    scopus 로고
    • Mixed-mode dynamics and the canard phenomenon: Towards a classification
    • Popović N 2008 Mixed-mode dynamics and the canard phenomenon: Towards a classification J. Phys.: Conf. Ser. 138 012020
    • (2008) J. Phys.: Conf. Ser. , vol.138 , Issue.1 , pp. 012020
    • Popović, N.1
  • 24
    • 34249880482 scopus 로고    scopus 로고
    • Regularization of discontinuous vector fields on via singular perturbation
    • Teixeira M A, Llibre J and da Silva P R 2007 Regularization of discontinuous vector fields on via singular perturbation J. Dyn. Diff. Eqns. 19 309-31
    • (2007) J. Dyn. Diff. Eqns. , vol.19 , Issue.2 , pp. 309-331
    • Teixeira, M.A.1    Llibre, J.2    Da Silva, P.R.3
  • 25
    • 0026239399 scopus 로고
    • Chaotic spikes arising from a model of bursting in excitable membranes
    • Terman D 1991 Chaotic spikes arising from a model of bursting in excitable membranes SIAM J. Appl. Math. 51 1418-50 (Pubitemid 21708816)
    • (1991) SIAM Journal on Applied Mathematics , vol.51 , Issue.5 , pp. 1418-1450
    • Terman David1
  • 26
    • 0000873906 scopus 로고
    • On 'relaxation oscillations'
    • Van der Pol B 1926 On 'relaxation oscillations' Phil. Mag. Ser. 2 978-92
    • (1926) Phil. Mag. Ser. , vol.2 , pp. 978-992
    • Van Der Pol, B.1
  • 27
    • 32044436353 scopus 로고    scopus 로고
    • 3 in the case of a folded node
    • DOI 10.1137/030601995
    • Wechselberger M 2005 Existence and bifurcation of canards in in the case of a folded node SIAM J. Appl. Dyn. Syst. 4 101-39 (Pubitemid 43385188)
    • (2005) SIAM Journal on Applied Dynamical Systems , vol.4 , Issue.1 , pp. 101-139
    • Wechselberger, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.